Scale-free network with Boolean dynamics as a function of connectivity

In this work we analyze scale-free networks with different power-law spectra N(k)similar tok(-gamma) under a Boolean dynamic, where the Boolean rule that each node obeys is a function of its connectivity k. This is done by using only two logical functions (AND and XOR) which are controlled by a parameter q. Using a damage spreading technique we show that the Hamming distance and the number of 1's exhibit power-law behavior as a function of q. The exponents appearing in the power laws depend on the value of gamma.